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The notion of r-stackedness for simplicial polytopes was introduced byMcMullen and Walkup in 1971 as a generalization of stacked polytopes. In thispaper, we define the r-stackedness for triangulated homology manifolds andstudy their basic properties. In addition, we find a new necessary conditionfor face vectors of triangulated manifolds when all the vertex links arepolytopal.

On r-stacked triangulated manifolds